# Lesson 4

Square Roots on the Number Line

Let’s approximate square roots.

### Problem 1

1. Find the exact length of each line segment.

2. Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning.

### Problem 2

Plot each number on the $$x$$-axis: $$\sqrt{16},\text{ } \sqrt{35},\text{ } \sqrt{66}$$. Consider using the grid to help.

### Problem 3

Use the fact that $$\sqrt{7}$$ is a solution to the equation $$x^2 = 7$$ to find a decimal approximation of $$\sqrt{7}$$ whose square is between 6.9 and 7.1.

### Problem 4

1. Explain how you know that $$\sqrt{37}$$ is a little more than 6.

2. Explain how you know that $$\sqrt{95}$$ is a little less than 10.

3. Explain how you know that $$\sqrt{30}$$ is between 5 and 6.

### Problem 5

Plot each number on the number line: $$\displaystyle 6, \sqrt{83}, \sqrt{40}, \sqrt{64}, 7.5$$

### Problem 6

The equation $$x^2=25$$ has two solutions. This is because both $$5 \boldcdot 5 = 25$$, and also $$\text-5 \boldcdot \text-5 = 25$$. So, 5 is a solution, and also -5 is a solution.

Select all the equations that have a solution of -4:

A:

$$10+x=6$$

B:

$$10-x=6$$

C:

$$\text-3x=\text-12$$

D:

$$\text-3x=12$$

E:

$$8=x^2$$

F:

$$x^2=16$$

### Problem 7

Find all the solutions to each equation.

1. $$x^2=81$$
2. $$x^2=100$$
3. $$\sqrt{x}=12$$

### Problem 8

The points $$(12, 23)$$ and $$(14, 45)$$ lie on a line. What is the slope of the line?

(From Unit 5, Lesson 4.)